Peter Takac
Abstract:
We study the Neumann boundary value problem for stationary radial
solutions of a quasilinear Cahn-Hilliard model in a ball
in
.
We establish new results on
the existence, uniqueness, and multiplicity (by "branching") of
such solutions. We show striking differences in pattern formation
produced by the Cahn-Hilliard model with the p-Laplacian and a
potential
()
in place of the
regular (linear) Laplace operator and a
potential. The
corresponding energy functional exhibits one-dimensional
continua ("curves") of critical points as opposed to the
classical case with the Laplace operator. These facts offer a
different explanation of the "slow dynamics" on the attractor
for the dynamical system generated by the corresponding
time-dependent parabolic problem.